Search Results (329)

This study explores the potential of wind energy to address electricity shortages in South Africa, focusing on the Ekuphumleni community in Whittlesea. Given the challenges of expanding the national grid to these areas, wind energy is considered to be a feasible alternative to provide clean, renewable energy and reduce fossil fuel dependence in this community. This research evaluates wind potential utilizing the two-parameter Weibull distribution, with scale and shape parameters estimated by five traditional numerical methods and one metaheuristic optimization technique: whale optimization algorithm (WOA). Goodness-of-fit tests, such as the coefficient of determination (R²) and wind power density error (WPDE), were utilized to determine the best method for accurately estimating Weibull scale and shape parameters. Furthermore, net fitness, which combines R² and WPDE, was employed to provide a holistic assessment of overall performance. Whittlesea showed moderate wind speeds, averaging 3.88 m/s at 10 m above ground level (AGL), with the highest speeds in winter (4.87 m/s) and optimum in July. The WOA method outperformed all five numerical methods in this study in accurately estimating Weibull distribution parameters. Interestingly, the openwind method (OWM), a numerical technique based on iterative methods, and the Brent method showed comparable performance to WOA. The wind power density was 67.29 W/m², categorizing Whittlesea’s potential as poor and suitable for small-scale wind turbines. The east wind patterns favor efficient turbine placement. The study recommends using augmented wind turbines for the site to maximize energy capture at moderate speeds. Full article

The weighted flexible Weibull distribution focuses on its unique point of flaunting a bathtub-shaped hazard rate, characterized by an initial increase followed by a drop over time. This property plays a major role in reliability analysis. In this paper, this distribution and its main properties are examined, and the parameters are estimated using several estimation methods. In addition, a simulation study is done for different sample sizes. The performance of the proposed model is illustrated through two real-world applications: component failure times and COVID-19 mortality. Moreover, the value-at-risk (VaR), tail value-at-risk (TVaR), peaks over a random threshold VaR (PORT-VaR), the mean of order P (${\mathrm{MOP}}_{\left[P\right]}$) analysis, and optimal order of P due to the true mean value can help identify and characterize critical events or outliers in failure events and COVID-19 death data across different counties. Finally, the PORT-VaR estimators are provided under a risk analysis for both applications. Full article

This study develops a new method for generating families of distributions based on the alpha power transformation and the trigonometric function, which enables enormous versatility in the resulting sub-models and enhances the ability to more accurately characterize tail shapes. This proposed family of distributions is characterized by a single parameter, which exhibits considerable flexibility in capturing asymmetric datasets, making it a valuable alternative to some families of distributions that require additional parameters to achieve similar levels of flexibility. The sine alpha power generated family is introduced using the proposed method, and some of its members and properties are discussed. A particular member, the sine alpha power-Weibull (SAP-W), is investigated in depth. Graphical representations of the new distribution display monotone and non-monotone forms, whereas the hazard rate function takes a reversed J shape, J shape, bathtub, increasing, and decreasing shapes. Various characteristics of SAP-W distribution are derived, including moments, rényi entropies, and order statistics. Parameters of SAP-W are estimated using the maximum likelihood technique, and the effectiveness of these estimators is examined via Monte Carlo simulations. The superiority and potentiality of the proposed approach are demonstrated by analyzing three real-life engineering applications. The SAP-W outperforms several competing models, showing its flexibility. Additionally, a novel-log location-scale regression model is presented using SAP-W. The regression model’s significance is illustrated through its application to real data. Full article

Accurately determining the exposure time to an infectious pathogen, together with the corresponding incubation period, is vital for identifying infection sources and implementing targeted public health interventions. However, real-world outbreak data often include outliers—namely, tertiary or subsequent infection cases not directly linked to the initial source—that complicate the estimation of exposure time. To address this challenge, we introduce a robust estimation framework based on a three-parameter Weibull distribution in which the location parameter naturally corresponds to the unknown exposure time. Our method employs a $\gamma$-divergence criterion—a robust generalization of the standard cross-entropy criterion—optimized via a tailored majorization–minimization (MM) algorithm designed to guarantee a monotonic decrease in the objective function despite the non-convexity typically present in robust formulations. Extensive Monte Carlo simulations demonstrate that our approach outperforms conventional estimation methods in terms of bias and mean squared error as well as in estimating the incubation period. Moreover, applications to real-world surveillance data on COVID-19 illustrate the practical advantages of the proposed method. These findings highlight the method’s robustness and efficiency in scenarios where data contamination from secondary or tertiary infections is common, showing its potential value for early outbreak detection and rapid epidemiological response. Full article

This study proposes a generalized family of distributions to enhance flexibility in modeling complex engineering and biomedical data. The framework unifies existing models and improves reliability analysis in both engineering and biomedical applications by capturing diverse system behaviors. We introduce a novel hybrid family of distributions that incorporates a flexible set of hybrid functions, enabling the extension of various existing distributions. Specifically, we present a three-parameter special member called the hybrid-Weibull–exponential (HWE) distribution. We derive several fundamental mathematical properties of this new family, including moments, random data generation processes, mean residual life (MRL) and its relationship with the failure rate function, and its related asymptotic behavior. Furthermore, we compute advanced information measures, such as extropy and cumulative residual entropy, and derive order statistics along with their asymptotic behaviors. Model identifiability is demonstrated numerically using the Kullback–Leibler divergence. Additionally, we perform a stress–strength (SS) reliability analysis of the HWE under two common scale parameters, supported by illustrative numerical evaluations. For parameter estimation, we adopt the maximum likelihood estimation (MLE) method in both density estimation and SS-parameter studies. The simulation results indicated that the MLE demonstrates consistency in both density and SS-parameter estimations, with the mean squared error of the MLEs decreasing as the sample size increases. Moreover, the average length of the confidence interval for the percentile and Student’s t-bootstrap for the SS-parameter becomes smaller with larger sample sizes, and the coverage probability progressively aligns with the nominal confidence level of 95%. To demonstrate the practical effectiveness of the hybrid family, we provide three real-world data applications in which the HWE distribution outperforms many existing Weibull-based models, as measured by AIC, BIC, CAIC, KS, Anderson–Darling, and Cramer–von Mises criteria. Furthermore, the HLW exhibits strong performance in SS-parameter analysis. Consequently, this hybrid family holds immense potential for modeling lifetime data and advancing reliability and survival analysis. Full article

In this paper, two different families are mixed: the exponentiated and new Topp–Leone-G families. This yields a new family, which we named the mixture of the exponentiated and new Topp–Leone-G family. Some statistical properties of the proposed family are obtained. Then, the mixture of two exponentiated new Topp–Leone inverse Weibull distribution is introduced as a sub-model from the mixture of exponentiated and new Topp–Leone-G family. Some related properties are studied, such as the quantile function, moments, moment generating function, and order statistics. Furthermore, the maximum likelihood and Bayes approaches are employed to estimate the unknown parameters, reliability and hazard rate functions of the mixture of exponentiated and new Topp–Leone inverse Weibull distribution. Bayes estimators are derived under both the symmetric squared error loss function and the asymmetric linear exponential loss function. The performance of maximum likelihood and Bayes estimators is evaluated through a Monte Carlo simulation. The applicability and flexibility of the MENTL-IW distribution are demonstrated by well-fitting two real-world engineering datasets. The results demonstrate the superior performance of the MENTL-IW distribution compared to other competing models. Full article

Wind energy is a clean, inexhaustible resource with significant potential to reduce coal dependence, lower carbon emissions, and provide sustainable energy in the off-grid areas of South Africa’s Eastern Cape. However, due to wind variability, site-specific assessments are crucial for accurate resource estimation and investment risk mitigation. This study evaluates the wind energy potential at Fort Hare using six statistical distribution models: Weibull (WEI), Rayleigh (RAY), gamma (GAM), generalized extreme value (GEV), inverse Gaussian (IGA), and Gumbel (GUM). The analysis is based on three years (2021–2023) of hourly wind speed data at 10 m above ground level from the Fort Beaufort weather station. Parameters were estimated using the maximum likelihood method (MLM), and model performance was ranked using the total error (TE) metric. The results indicate an average wind speed of 2.60 m/s with a standard deviation of 1.85 m/s. The GEV distribution was the best fit (TE = 0.020), while the widely used Weibull distribution ranked third (TE = 0.5421), highlighting its limitations in capturing wind variability and extremes. This study underscores the importance of testing multiple models for accurate wind characterization and suggests improving the performance of the Weibull model through advanced parameter optimization, such as artificial intelligence. The wind power density was 31.52 W/m², classifying the site as poor for large-scale electricity generation. The prevailing wind direction was southeast. Recommendations include deploying small-scale turbines and exploring augmentative systems to optimize wind energy utilization in the region. Full article

Currently, Industry 4.0 creates new opportunities for analyzing data on production processes and extracting knowledge from them. With the Internet of Things, data is continuously collected from machine sensors to analyze machine health. Thanks to artificial intelligence methods and discrete simulation, it is possible to process data and dynamically adjust the operating conditions of the production line to the expected time of failure-free operation of the machine or reliable work of an employee. Recently, machine learning techniques have been used to automatically adapt the production line to changes in a given production environment. The paper presents various methods of modeling actions, i.e., forecasting the failure-free operation time of a machine or the error-free working time of an employee. The possible actions the agent can perform, the possible prediction techniques that can be selected are presented. The time between failures is described by a log-normal distribution. The asymmetric lognormal distribution is much more flexible for practical modeling compared to the “perfectly” symmetric normal distribution. In practice, the asymmetric lognormal distribution, strongly shifted to the left, can be used to describe the decreasing time between failures due to human error, as well as the time between failures of a machine in the third phase of its life cycle, which decreases as the machine ages and its components wear out. The parameters of the distribution are estimated using the maximum-likelihood approach, theempirical moments approach, the renewal-theory approach, the empirical distribution function and the method based on coefficient of variation. Numerical examples of predicting failure-free operation times described by the log-normal distribution are presented. The results are compared assuming that failure-free times are described by exponential, normal and Weibull distributions. The results are also compared with an example of the simplest learning method. Full article

This study introduces two bivariate extensions of the recently proposed weighted discretized Fréchet–Weibull distribution, termed as bivariate weighted discretized Fréchet–Weibull (BWDFW) distributions. These models are specifically designed for analyzing two-dimensional discrete datasets and are developed using two distinct structural approaches: the minimum operator (BWDFW-I) and the maximum operator (BWDFW-II). A rigorous mathematical formulation is presented, encompassing the joint cumulative distribution function, joint probability mass function, and joint (reversed) hazard rate function. The dependence structure of the models is investigated, demonstrating their capability to capture positive quadrant dependence. Additionally, key statistical measures, including covariance, Pearson’s correlation coefficient, Spearman’s rho, and Kendall’s tau, are derived using the joint probability-generating function. For robust statistical inferences, the parameters of the proposed models are estimated via the maximum likelihood estimation method, with extensive simulation studies conducted to assess the efficiency and accuracy of the estimators. The practical applicability of the BWDFW distributions is demonstrated through their implementation in two real-world datasets: one from the aviation sector and the other from the security and safety domain. Comparative analyses against four existing discrete bivariate Weibull extensions reveal the superior performance of the BWDFW models, with BWDFW-I (minimum operator based) exhibiting greater flexibility and predictive accuracy than BWDFW-II (maximum operator based). These findings underscore the potential of the BWDFW models as effective tools for modeling and analyzing bivariate discrete data in diverse applied contexts. Full article

The watershed of the Peixe River lies in central Minas Gerais state, close to Belo Horizonte city, a densely populated area. The area is located in the geological context of Quadrilátero Ferrífero, one of the most prominent mineral provinces in Brazil. To better recognize surface and groundwater availability, some methodologies have been applied to evaluate the minimal surface flow rates, groundwater recharge, and water reserves. The basin includes three main aquifer systems: Cauê (porous and fissured aquifer), related to iron formations; Gandarela, related to karst-fissured rocks; and Cercadinho, related to metapelite rocks. The Cauê aquifer presented the highest effective porosity and hydraulic conductivity. In contrast, the Cercadinho aquitard shows the lowest hydrodynamic parameters. Data between the years of 2004 and 2024 from 21 pumping tests from wells associated with the three aquifer systems were obtained to estimate the respective recharge rate. The recharge was evaluated by numeric recursive filter and recession-curve displacement methods. The recharge results with the numeric filter method showed underestimated values. Regarding the recession-curve displacement method, the results were more consistent with other studies in the surroundings. The average recharge estimated for the basin represents 24% to 54% of annual pluviometry in the hydrological periods of analysis. The recharge data were accounted for in the reserves calculation, including permanent and renewable reserves. Total permanent reserves were estimated to be 3.16 × 10⁹ m³, including the prior aquifer systems of Cauê, Gandarela, and Cercadinho. The total mean renewable reserves of the basin were calculated to be 4.55 × 10⁷ m³/year in the analyzed period. The high BFImax indexes found in baseflow separation, above 90%, suggest a relevant contribution of the karstic Gandarela aquifer on the watershed surface flow. Although in some years it has been concluded that groundwater exploitation outlines the renewable resources availability, in 2024’s scenario, the granted water volume was lower than the estimated availability and reserves. The best methodologies for coupling surface and groundwater are the Weibull distribution for reference surface flows and the recessive-curve displacement for baseflow separations. This research will be a contribution to water resources management strategies for regions with high population growth and water demand increase. Full article

Accurate drought identification is important for both scientists and decision-makers to be able to make informative decisions. In this study, parametric and non-parametric approaches for analyzing meteorological drought are compared, aiming at simplifying the calculation of the Standardized Precipitation Index (SPI). The comparison is performed across various meteorological stations covering the entire territory of Greece, using monthly rainfall data spanning from 1961 to 2021. Meteorological drought is assessed through the SPI for the 12-month reference period. A two-parameter gamma distribution, with parameters estimated using the maximum likelihood estimation method, is employed for the estimation of the SPI drought index as the parametric classic approach. For the non-parametric approach, the SPI drought index is estimated using six empirical probability plotting positions: Beard, Blom, Cunnane, Gringorten, Hazen, and Weibull. Results indicate that the empirical approach can effectively identify drought events in comparison to the classic approach. However, caution is advised, particularly when different drought classes are identified, as the non-parametric approaches may underestimate drought severity. In addition, for the Greek meteorological conditions, the results revealed that in the case of extreme drought events, the estimation of SPI employing the classic approach is to be preferred. Full article

In the first part of this article devoted to the assessment of the fatigue life of structural steels at low temperatures, a study was conducted on the effect of pre-cycling in a low-cycle fatigue mode on the time dependences of acoustic emission parameters. Commonly used St-3 steel was tested at −60 °C with varying durabilities, after which it was fractured once during static tests. The multilevel acoustic model used made it possible to estimate the structural parameter $\gamma$ at the stage of elastoplastic deformation. The stage of active development of microcracks and their coalescence corresponds to a homogeneous fracture with stable acoustic emission characteristics (signal duration, amplitude variation coefficient, etc.). It was shown that regardless of the maximum voltage (460, 480, and 500 MPa) in the cycle and the operating times of up to 0.3, 0.5, and 0.7, the structural parameter remains within the known limits. The parameters of the Weibull law distribution and the logarithmically normal distribution for the coefficient γ were obtained, theoretical and calculated fatigue curves were plotted, and a method was proposed for evaluating the number of cycles before fracture under irregular loading conditions in the real operation of pressure vessels based on the “rainflow” cycles counting method. Full article

The exponentiated exponential distribution has received great attention from many statisticians due to its popularity, many applications, and the fact that it is an efficient alternative to many famous distributions such as Weibull and gamma distributions. Many statisticians have studied the mathematical properties of this distribution and estimated its parameters under different censoring schemes. However, it seems that the distribution of the random sum, the distribution of the linear combination, and the value of the reliability index, $R=P(X_2<X_1)$, in the case of unequal scale parameters, were not known for this distribution. Therefore, in this article, we present the saddlepoint approximation to the distribution of the random sum, the distribution of linear combination, and the value of the reliability index $R=P(X_2<X_1)$ for exponentiated exponential variates. These saddlepoint approximations are computationally appealing, and numerical studies confirm their accuracy. In addition to the accuracy provided by the saddlepoint approximation method, it saves time compared to the simulation method, which requires a lot of time. Therefore, the saddlepoint approximation method provides an outstanding balance between precision and computational efficiency. Full article

Given the increasing number of phenomena that demand interpretation and investigation, developing new distributions and families of distributions has become increasingly essential. This article introduces a novel family of distributions based on the exponentiated reciprocal of the hazard rate function named the new Lomax-G family of distributions. We demonstrate the family’s flexibility to predict a wide range of lifetime events by deriving its cumulative and probability density functions. The new Lomax–Weibull distribution (NLW) is studied as a sub-model, with analytical and graphical evidence indicating its efficiency for reliability analysis and complex data modeling. The NLW density encompasses a variety of shapes, such as symmetrical, semi-symmetrical, right-skewed, left-skewed, and inverted J shapes. Furthermore, its hazard function exhibits a broad range of asymmetric forms. Five estimation techniques for determining the parameters of the proposed NLW distribution include the maximum likelihood, percentile, least squares, weighted least squares, and Cramér–von Mises methods. The performance of the estimators of the studied inferential methods is investigated through a comparative Monte Carlo simulation study and numerical demonstration. Additionally, the effectiveness of the NLW is validated by means of four real-world datasets. The results indicate that the NLW distribution provides a more accurate fit than several competing models. Full article

Animal experiments have long been used as an educational tool in pharmacological education; however, from the perspective of animal welfare, it is necessary to decrease the number of animals used. ingAlthough using of simulators is effective, the development of these simulators is necessary when there is no existing simulator for animal experiments. In this review, we describe free, downloadable, and commercial simulators that are currently used in pharmacological education. Furthermore, we introduce two strategies to create simulators of animal experiments: (1) bioassay, and (2) experiments that measure the reaction time. We also describe five sigmoid curves (logistic curve, cumulative distribution function [CDF] of normal distribution, Gompertz curve, von Bertalanffy curve, and CDF of Weibull curve) to fit the results and their inverse functions. Using this strategy, it is possible to create a simulator that calculates the reaction time following drug administration. Moreover, we introduce a statistical model for local anesthetic agents using hierarchical Bayesian modeling. Considering the correlation among estimated parameters, we suggest it is possible to create simulators that give results more similar to those of animal experiments. The pharmacological education will be possible by these simulators at educational institutions where animal experiments are difficult due to various restrictions. It is expected that the number of simulator-based education programs will increase in the future. Full article